Tilt meter

ABSTRACT

A tilt meter is provided with a horizontally disposed beam that supports on its underside a pair of spaced liquid containers. Insulated electrodes are supported and spaced above each liquid surface and connected to the underside of the beam. The liquids are electrically conductive. A first pipe is provided to communicate the liquid in one container with the liquid in the other container, and a second pipe is provided to communicate the space above each liquid surface with that space above the other.

United States Patent Stacey et al.

[ TILT METER [72] Inventors: Frank Donald Stacey, Kenmore;

John Munro William Rynn, Annerley, both of Australia; Eric CooperLittle, Moggill, Great Britain; Clyde Croskell, Taringa, Australia [73]Assignee: The Universtity of Queensland, St.

Lucia, Brisbance, Queensland, Australia [22] Filed: Jan. 8, 1971 [21]App]. N0.: 105,102

Related US. Application Data [63] Continuation of Ser. No. 758,720,Sept. 10,

1968, abandoned.

[52] US. Cl. ..33/366, 73/398, 33/368 [51] Int. Cl. ..G0lc 9/22 [58]Field of Search....33/209, 206.5; 73/393, 398 C, 73/497, 125 T; 317/247[56] References Cited UNlTED STATES PATENTS 2,814,127 11/1957 Blatchford..33/209 2,532,883 12/1950 Bennett et a1. ..33/209 2,679,758 6/1954 Lambet a1 ..73/363.9 3,140,613 7/1964 Hasegawa ..73/393 [451 Oct. 17,1972

3,225,599 12/1965 Schwien ..73/398 C 3,471,780 10/1969 Beddows ..317/2462,532,883 12/1950 Bennett et a1. ..33/209 2,679,758 6/1954 Lamb et a1..73/363.9 2,907,321) 10/1959 De Weese et al. ..73/398 C 3,140,6137/1964 Hasegawa ..73/393 3,225,599 12/1965 Schwien ..73/398 C OTHERPUBLICATIONS Rawlings, A. L. The Theory of the Gyroscopic Cornpass, TheMacMillan Company 1944, pp. 40- 52.

Primary Examiner-Leonard Forman Assistant Examiner--Dennis A. DearingAttorney-Waters, Roditi, Schwartz & Nissen s7 ABSTRACT 13 Claims, 5Drawing Figures H 20 190 las 26 13 19.-- -19 19 4s as g 1 I g 12 112 2'41'8 PATENTEDnm 11 m2 SHEET 3 [1F 3 This application is a continuation ofapplication, Ser. No. 758,720 filed Sept. 10, 1968 and now abandoned.

This invention relates to the measurement of tilt or departure from thehorizontal of a surface or between two reference marks and isspecifically directed to apparatus of extreme sensitivity.

Such tilt meters are necessary in geophysical work where the tilt withtime of the earths surface is to be measured.

It is an object of this invention to provide apparatus with asensitivity of the order of 7 to 10-9 radians.

It is a further object to provide such apparatus in a portable form.

The invention uses the principle of measuring tilt between two spacedreference surfaces by comparison of the capacities between a liquidsurface and electrodes mounted on a rigid member supported on saidsurfaces.

Accordingly, the invention comprises a tilt meter for measuring tiltbetween two spaced reference surfaces, including a support contactingeach said surface, a rigid member supported between said supports, atleast one container attached beneath said rigid member, insulatedelectrodes attached at spaced positions on said rigid member above saidcontainers, a conducting liquid in said container, the surface of saidliquid lying below each said electrode, and electrical means indicatingthe ratio of capacities between said surface and the respectiveelectrodes.

Preferably the container is in the form of two pools, one below eachelectrode, having a liquid connection between them.

The container or each pool may besealed to said member to preventspillage of the liquid during transport or displacement of the member.

Compensation may be provided to prevent variations in temperature fromaffecting the capacity ratio.

In order that the invention may be better understood it willbe discussedwith reference to the accompanying drawings of exemplary arrangements,in which:

FIG. 1 shows a, partly broken away, side view of one form of theapparatus,

FIG. 2 shows a plan view of the apparatus of FIG. 1,

FIG. 3 shows, in enlarged'scale, a section through one of the electrodeand pool assemblies of FIG. 1,

FIG. 4 showsa modification of the arrangement of FIG. 3, and

FIG. 5 shows a block circuit of the electrical system used.

Referring first to FIGS. 1 and 2, a rigid member comprising a bar orbeam 10, preferably of stainless steel, is mounted on the referencesurfaces 11, 12 on supports comprising fixed legs 13, 14 contactingsurface 11 and a single leg 15 contacting surface 12. Bar or beam 10 hasinsulated electrodes 16 mounted at spaced posi' tions along its length.

On the lower surface of beam 10 beneath electrodes 16 is a liquidcontainer comprising separate pools 17 for containing mercury connectedby a pipe 21.

Each pool is mounted on a base-plate 18, supported from the beam 10 bypillars 19. As will be described below, temperature-compensation meansare provided in the pool assembly.

Nitrogen or other inert gas lies above the mercury in the pools 17 'toprevent oxidation.

A nitrogen tube 20 connects the spaces above the mercury in pools 17,and tube 21 connects the bodies of mercury in the pools. The tubes 20,21 are curved (FIG. 2) to avoid straining the pools 17, and the bore oftube 20 is made such that oscillation of mercury is critically damped.

The apparatus functions generally by comparing the capacities betweenthe mercury surface level in pools 17 and the respective electrodes 16,to measure the tilt of beam 10. A ratio-transformer bridge circuit isused (as will be later explained), a' pre-amplifier 22 being mounted onthe beam and connected to the mercury in line 21. A heavy metal shield24 attached to the beam electrically shields the apparatus.

Various features of the apparatus will now be described in more detail.

THE MERCURY SYSTEM where C= Po/2S and B rg/S= 2.8 X 10 121' There is asimple series solution In the range of interest (x 2.5 cm, Cx 200), y isvery close to an exponential dependent on x y=A exp (5101:)

Where A is a constant including A and determined by the boundaryconditions at the pool edge where dy/dx l and and x D/2 (D is the pooldiameter). For D= 8 cm, A 2.7 X 10- cm and atx= 2.5 cm (i.e., at theedge of an electrode of 5 cm diameter), y 2 X 10' cm. This about 2 X 10of the mean capacitance gap G, and is of negligible effect on thereadings.

Similarly, other relative diameters of the electrode and the pool may becalculated to give substantial flatness. The formula is obviouslyapplicable for liquids other than mercury.

The depth of mercury in pools 17 is kept as small as possible tominimize the effect of thermal expansion, but the minimum depth islimited by the requirement that capillarity should not prevent completeand automatic refilling of the tube 21 after emptying.

This minimum depth from the mercury surface to tube 21 is given by:

h (4 S cos A)/(rgd) where S surface tension of Hg,

r= density of Hg,

g= acceleration due to gravity,

d= bore of tube 21,

A angle of contact of Hg (for stainless steel pool, A

For d=2.6mm, h is 6mm.

The bore of mercury tube 21 is chosen to give the desired hydraulicresponse; for most purposes the condition for critical damping isrequired. This is given by:

n viscosity of Hg,

l= length of tube 21,

D= diameter of pools 17,

and g, r and d as before.

For l= 40cm, D 8cm, d is about 2.3mm.

This gives a hydraulic response time of about 4 seconds which issufficiently short for the instrument to respond well to seismic waves.

With the accuracies involved, it is necessary to prevent any oxidationof the mercury and ensure that the pressures above it in pools 17 beequal. A dry, oxygen-free nitrogen (or other inert gas) filling is usedand nitrogen tube 20 ensures equal pressures. Filling of pools 17 withmercury is effected by scalable fillers 25,

26, through which the nitrogen atmosphere may also be introduced. Byintroducing a gas flow at 25 to emerge at 26 the system can be flushedto ensure removal of all air and oxygen.

TEMPERATURE COMPENSATION The gap G between the mercury surface and anelectrode 16 should be kept at constant temperature for the range ofambient temperatures over which the instrument is required to operate.

This may be accomplished by using the different temperature coefficientsof expansion of different materials.

Referring to FIG. 3, pool 17 is sealed to the beam 10 by alow-dielectric resilient material (such as silicone rubber) at 27 sothat it may move slightly with respect to beam 10.

The gap G depends on the expansion coefficients of the stainless steelspacers 19, silica pillars 28 and the mercury in pool 17. For a constantG:

1 d2 em Where a a, and a are the volume expansion coefficient of mercuryand the linear coefficients of stainless steel, and silica respectively,

D is the diameter of pool 17,

t is the length of pillars 28,

a is the depth of Hg,

and l, d are the length and bore of tube 21.

If D 8cm, 6mm, G 1.0mm, l= 33.5cm, d= 2.3mm then t= 4.63cm.

It will be appreciated that expansion of spacers 19 tends to increasegap G, while expansion of pillars 28 tends to decrease it.

Similarly increase of temperature expands the mercury in container 17,tending to reduce the gap and expands the container itself tending toincrease it. Using the relation given above, these factors cancel togive a constant G.

The length S of spacers 19 is about 6.2cm.

It is clear that a similar relation holds for materials other thanstainless steel, silican and mercury.

Error in temperature compensation may arise from error in a,, but evenallowing an error of 6 percent in this (10 times the quoted tolerance),the spurious tilt per C. is 4 X 10 (R 0.5) where R is theratio-transformer reading at balance (0 R l For high-sensitivitymeasurements, (R 0.5) is arranged to be less than 10' so the error perC. is not greater than 4 X l0" radian.

A similar temperature-compensation effect may be obtained with themodification shown in FIG. 4.

Here circular pool 17 is mounted on a resilient block 29 on base-platel8 and spaced from beam 10 by silica spacers 30. Its position isunaffected by temperature expansion of spacers l9 and its upper edgeposition is governed by silica spacers 30.

A cylindrical silica block 31 of diameter D, and height h, is immersedin the mercury.

By suitably dimensioning the length b of spacers 30 and diameter andheight of the block 31, a temperature rise dT causes an increase in thedimension (m +b) equal to the rise in mercury level, so keeping gapwidth G constant.

Thus (m-a, bud) dT (Volume change of Hg and Si relative to steel) li lill! This enables temperature-compensation to be calculated for any givenconditions.

A temperature difference between the ends of beam 10 as small as 10" C.at highest sensitivity may give a significant spurious tilt reading.

The bridge comparison and pool temperature compensation however allow anoverall length of beam only of the order of 50cm to be used. Theinstrument is therefore small enough to be completely enclosed inthermal shields (not shown) when installed.

between its ends, so that effective heat shielding is easily obtained.

THE LEG MOUNTINGS Beam is mounted on legs l3, 14, which engage onprepared rock surfaces ll, 12. These surfaces are normally prepared togive an initial horizontal beam position with the fixed legs shown.

However, the legs may be made slightly variable in length either byscrew adjustments, or by mounting the single leg 15 on amicrometer-controlled lever forvery fine adjustment. These modificationsare, however, not shown in the drawings.

It is important that the precise points on which the legs rest remainthe same in spite of any expansion or contraction of the beam 10 or therock.

Legs 13, 14, 15 are therefore made sufficiently flexible to accommodatesuch movements without frictional sliding of the points of support.

Assuming a circular leg of length L, diameter x and Youngs modulus q,supporting a mass M/2 with a coefficient of friction u, the slidingthereof is prevented if:

ELECTRICAL FIG. 5 shows in block form the electrical circuit of theinstrument, which compares the capacities between the electrodes 16 andthe mercury surface in pools 17 by means of a ratio-transformer bridge(A.M. Thomson: IRE Trans on lnstr 1-7 (3 and 4) p. 246253).

An oscillator 32 through input transformer 33, feeds a ratio-transformer33 which is connected to electrodes 16 via leads 34, 35 (see also FIG.1). The mercury (acting as the other electrode of the capacities C1, C2)is connected to the input of a high-impedance preamplifier 22 mounted ina recess on the beam 10 (FIG. 1). Output from 22 is fed via amplifier 36to detector 37 and recorder 38.

The ratio-transformer gives a voltage ratio accurate to about 1 part in10 against environmental changes when supplied from oscillator 32 atabout 2 3 KHz. and 5 ohms source impedance.

in one system of operation, the ratio is adjusted (by five decade dialsplus a potentiometer for sixth and seventh decades) to a null readingsensed by detector 37.

.ln this operation, many readings are necessary to give a time versustilt record, but the system is free of error due to extraneousconditions, such as power supply or oscillator amplitude and frequencyvariations, gain in amplifiers 22, 36 etc.

A more usual system of operation is to set the ratiotransformer to anarbitrary reference zero and record the off-balance signal versus time.

Such unbalanced operation places restrictions on the electronicequipment, as follows:

Oscillator 32 must be of constant amplitude. If an inductor is used fromtrough to ground, as it may be to increase sensitivity, oscillatorfrequency must also be constant. The output impedance of inputtransformer 33 must be low, so that output does not vary with loadvariation due to tilt.

The DC. output of detector 37 must exactly represent the A.C. input. Asynchronous detector fed by reference voltage via lead 39 from the A.C.source is ideal, giving oppositepolarity of output for tilt variationsin opposite sense.

The gain of amplifiers 22 and 36 must be constant.

The input impedance of 22 should be high, and the preamplifier 22 maywith advantage use field effect transistors.

The power-supply to the equipment will normally be stabilized.

If the ratio of the two parts of transformer 33 is R (l-R), where 0 R l(R)/( l-R) (C1 l/C2) (d2/dl) since capacitance is unversely proportionalto gap width (d1 or d2). Also the tilt angle 0 (d1 d2)/(L) where L=distance between electrodes 16 (2D/L) (R-0.5) where D= d] d2 a constant.

Thus the reading of the ratio-transformer is linear with tilt to a highdegree of first-order accuracy, the maximum error being of the order of0.05 percent of the reading.

By choosing L and D, direct readings in radians may be obtained from thedial settings of transformer 33. For D= 2mm, L 40cm; tilt (R 0.5) X 10radians. j i i A time-constant circuit 37 in the output of detector 37gives a cut-off at about 1c.p.s., and removes the effect of ripples orother short-term disturbances on the mercury surface.

The peak potentials applied between an electrode 16 and the mercurysurface must be low enough not to disturb that surface by electrostaticattraction. At balance (i.e., equal capacitor gaps) the effect is partlycompensated, but, when out of balance, the bridge voltage (V) should notexceed a value given by:

where G electrode gap e, permittivity r density of Hg 3 gravityacceleration dG= maximum deflection of Hg surface With a maximumtolerable spurious tilt of 10' radian on a baseline of 40cm, 416 is 4 X10' cm and V= 3 volts rrns.

Since neither the electrodes 16 or pools 17 are at earth (beam)potential, a stray capacities should be minimized and made equal. Theshield .24 (FIG. 1) is symmetrical with respect to the pool-electrodesystems and has as much clearance from these systems as possible.

Each electrode 16 is insulated from beam by a fluon or like sleeve 40(FIG. 3) sealed top and bottom by epoxy resin at 41, and each pool 17 isspaced from the beam at 27 by a silicone rubber or like low-dielectricseal. I

What is claimed is:

l. A tilt-meter comprising a rigid bar having a lower surface, said barbeing of a material having high heat conductivity; support means on saidbar for resting the bar on a reference surface whose horizontality is tobe determined; a pair of spaced containers; means securing thecontainers to said bar beneath said lower surface of said bar; anelectrically conductive liquid partly filling each of said containers toa predetermined level and providing a flat liquid surface in saidcontainers; liquid-tight sealing means between said containers and saidlower surface of said bar; electrodes supported by said bar at apredetermined height above the liquid level in said containers to definea gap of predetermined width between said electrodes and the liquid;insulating means electrically insulating said electrodes from said bar;a fluid medium contained within the gaps to normally maintain a constantpressure between said electrodes and the liquid and to prevent oxidationthereof; a first pipe interconnecting said containers for communicationof the liquid from one container to the other in response to tilting ofthe bar and containers; scalable filling means above the level of theliquid in said containers for effecting filling of saidelectricallyconductive liquid into said containers and filling of saidfluid medium into said gaps and arranged to maintain a closedcirculation system between said containers; electrical bridge means forindicating the ratio of capacities between the surface of said liquid ineach container and its respective electrode, .said bridge meansincluding a ratio-transformer constituting two arms of said bridge, saidcapacities constituting the remaining arms; an oscillator; low-impedancemeans electrically coupled with said oscillator and bridge means forfeeding input voltage to said bridge means; and adjustable detectormeans between said transformer and said capacities for establishingbalance in the bridge to enable determination of any angle of tilt ofthe bar and thereby of said reference surface in direct proportion tothe setting of the ratio transformer, said means securing the containersto the bar comprising temperature compensation means coupled with eachcontainer for adjusting the position of the container with respect tothe bar to maintain constant gap width between the electrodes and theliquid in the container for different ambient temperatures.

2. A tilt-meter as claimed in claim 1 in which said input voltage has anamplitude of less than =acceleration due to r vit 5 is the maximum a loiable deflection of the liquid surface dueto electrostatic attraction.

3. A tilt-meter as claimed in claim 1, wherein said electro-conductiveliquid is mercury.

4. A tilt-meter as claimed in claim 1, wherein said fluid medium is aninert gas.

5. A tilt-meter as claimed in claim 1, wherein said fluid medium isnitrogen. I

6. A tilt-meter as claimed in claim 1, wherein said pair of containerseach includes an upper edge engaging said lower surface of said bar, andwherein said liquid-tight sealing means is a low-dielectric sealsandwiched between said upper edge and said lower surface.

7. A tilt-meter as defined in claim 1, wherein said liquid-tight sealingmeans is made of silicone rubber.

8. A tilt-meter as defined in claim I, further comprising metallicshielding means secured to said lower sur face of said bar and enclosingsaid container for electrically shielding the latter.

9. A tilt-meter as defined in claim 1, wherein said first and secondpipes are curved such as to avoid straining of said containers, andwherein said second pipe has an inner diameter such as to criticallyreduce oscillation of said fluid medium.

10. A tilt-meter as claimed in claim 1 wherein said temperaturecompensation means comprises a block of solid material immersed in theliquid in each container and support means for each container from saidbar to compensate for variation of the gap produced by volume change ofthe liquid and the block in each container upon temperature variationwhereby said gap is maintained constant independently of temperature.

11. A tilt-meter as claimed in claim 1 wherein said means securing thecontainers to the bar comprises a base-plate beneath each saidcontainer, supports of a first material between said base-plate and saidbar; and spacer means of a second material between said baseplate andthe bottom surface of said container; said sealing means being resilientto allow movement between each said container and said bar.

12. A tilt-meter as claimed in claim 11 wherein said spacer means.comprises a resilient block, said support means further comprisingspacer elements between said containers and said bar.

13. A tilt-meter as claimed in claim 1 in which each said container andeach said electrode are circular and coaxially supported, each saidelectrode being of smaller diameter than its respective container so itoverlies only a flat portion of the surface of said liquid therein.

* a i: k

1. A tilt-meter comprising a rigid bar having a lower surface, said barbeing of a material having high heat conductivity; support means on saidbar for resting the bar on a reference surface whose horizontality is tobe determined; a pair of spaced containers; means securing thecontainers to said bar beneath said lower surface of said bar; anelectrically conductive liquid partly filling each of said containers toa predetermined level and providing a flat liquid surface in saidcontainers; liquidtight sealing means between said containers and saidlower surface of said bar; electrodes supported by said bar at apredetermined height above the liquid level in said containers to definea gap of predetermined width between said electrodes and the liquid;insulating means electrically insulating said electrodes from said bar;a fluid medium contained within the gaps to normally maintain a constantpressure between said electrodes and the liquid and to prevent oxidationthereof; a first pipe interconnecting said containers for communicationof the liquid from one container to the other in response to tilting ofthe bar and containers; sealable filling means above the level of theliquid in said containers for effecting filling of saidelectrically-conductive liquid into said containers and filling of saidfluid medium into said gaps and arranged to maintain a closedcirculation system between said containers; electrical bridge means forindicating the ratio of capacities between the surface of said liquid ineach container and its respective electrode, said bridge means includinga ratio-transformer constituting two arms of said bridge, saidcapacities constituting the remaining arms; an oscillator; low-impedancemeans electrically coupled with said oscillator and bridge means forfeeding input voltage to said bridge means; and adjustable detectormeans between said transformer and said capacities for establishingbalance in the bridge to enable determination of any angle of tilt ofthe bar and thereby of said reference surface in direct proportion tothe setting of the ratio transformer, said means securing the containersto the bar comprising temperature compensation means coupled with eachcontainer for adjusting the position of the container with respect tothe bar to maintain constant gap width between the electrodes and theliquid in the container for different ambient temperatures.
 2. Atilt-meter as claimed in claim 1 in which said input voltage has anamplitude of less than where G electrode to liquid surface gap eopermittivity of the gap r density of the liquid g acceleration due togravity dG is the maximum allowable deflection of the liquid surface dueto electrostatic attraction.
 3. A tilt-meter as claimed in claim 1,wherein said electro-conductive liquid is mercury.
 4. A tilt-meter asclaimed in claim 1, wherein said fluid medium is an inert gas.
 5. Atilt-meter as claimed in claim 1, wherein said fluid medium is nitrogen.6. A tilt-meter as claimed in claim 1, wherein said pair of containerseach includes an upper edge engaging said lower surface of said bar, andwherein said liquid-tight sealing means is a low-dielectric sealsandwiched between said upper edge and said lower surface.
 7. Atilt-meter as defined in claim 1, wherein said liquid-tight sealingmeans is made of silicone rubber.
 8. A tilt-meter as defined in claim 1,further comprising metallic shielding means secured to said lowersurface of said bar and enclosing said container for electricallyshielding the latter.
 9. A tilt-meter as defined in claim 1, whereinsaid first and second pipes are curved such as to avoid straining ofsaid containers, and wherein said second pipe has an inner diameter suchas to critically reduce oscillation of said fluid medium.
 10. Atilt-meter as claimed in claim 1 wherein said temperature compensationmeans comprises a block of solid material immersed in the liquid in eachcontainer and support means for each container from said bar tocompensate for variation of the gap produced by volume change of theliquid and the block in each container upon temperature variationwhereby said gap is maintained constant independently of temperature.11. A tilt-meter as claimed in claim 1 wherein said means securing thecontainers to the bar comprises a base-plate beneath each saidcontainer, supports of a first material between said base-plate and saidbar; and spacer means of a second material between said base-plate andthe bottom surface of said container; said sealing means being resilientto allow movement between each said container and said bar.
 12. Atilt-meter as claimed in claim 11 wherein said spacer means comprises aresilient block, said support means further comprising spacer elementsbetween said containers and said bar.
 13. A tilt-meter as claimed inclaim 1 in which each said container and each said electrode arecircular and coaxially supported, each said electrode being of smallerdiameter than its respective container so it overlies only a flatportion of the surface of said liquid therein.